Abstract
We consider cut games where players want to cut themselves off from different parts of a network. These games arise when players want to secure themselves from areas of potential infection. For the game-theoretic version of Multiway Cut, we prove that the price of stability is 1, i.e., there exists a Nash equilibrium as good as the centralized optimum. For the game-theoretic version of Multicut, we show that there exists a 2-approximate equilibrium as good as the centralized optimum. We also give poly-time algorithms for finding exact and approximate equilibria in these games.
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Notes
Recall that a (pure-strategy) Nash equilibrium is a solution where no single player can switch her strategy and become better off, given that the other players keep their strategies fixed.
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A preliminary version of this paper appeared in WAOA 2010.
This work was supported in part by NSF grants CCF-0914782 and CNS-1017932.
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Anshelevich, E., Caskurlu, B. & Hate, A. Strategic Multiway Cut and Multicut Games. Theory Comput Syst 52, 200–220 (2013). https://doi.org/10.1007/s00224-011-9380-1
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DOI: https://doi.org/10.1007/s00224-011-9380-1